What value will come in place of question mark(?) in the question
2`1/6`+2`1/66`+1`1/3`=?

Options

A. 14`115/34`
B. 5`17/33`
C. 6`17/35`
D. 4`1/3`

Answer

To solve the question \( 2 \frac{1}{6} + 2 \frac{1}{66} + 1 \frac{1}{3} = ? \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
1. Convert \( 2 \frac{1}{6} \):
\[ 2 \frac{1}{6} = \frac{2 \times 6 + 1}{6} = \frac{12 + 1}{6} = \frac{13}{6} \]

2. Convert \( 2 \frac{1}{66} \):
\[ 2 \frac{1}{66} = \frac{2 \times 66 + 1}{66} = \frac{132 + 1}{66} = \frac{133}{66} \]

3. Convert \( 1 \frac{1}{3} \):
\[ 1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{3 + 1}{3} = \frac{4}{3} \]

### Step 2: Find a Common Denominator
The denominators we have are 6, 66, and 3. The least common multiple (LCM) of these numbers is 198.

### Step 3: Convert Each Fraction to Have the Common Denominator
1. Convert \( \frac{13}{6} \) to a denominator of 198:
\[ \frac{13}{6} = \frac{13 \times 33}{6 \times 33} = \frac{429}{198} \]

2. Convert \( \frac{133}{66} \) to a denominator of 198:
\[ \frac{133}{66} = \frac{133 \times 3}{66 \times 3} = \frac{399}{198} \]

3. Convert \( \frac{4}{3} \) to a denominator of 198:
\[ \frac{4}{3} = \frac{4 \times 66}{3 \times 66} = \frac{264}{198} \]

### Step 4: Add the Fractions
Now we can add the fractions:
\[ \frac{429}{198} + \frac{399}{198} + \frac{264}{198} = \frac{429 + 399 + 264}{198} = \frac{1092}{198} \]

### Step 5: Simplify the Result
Now we simplify \( \frac{1092}{198} \):
\[ \frac{1092 \div 198}{198 \div 198} = \frac{5.5}{1} = 5 \frac{17}{99} \]

### Final Answer
Thus, the value that comes in place of the question mark (?) is:
\[ 5 \frac{17}{99} \]

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